Why should we be loyal to reason if it pushes us into the abyss?

Leibniz published books and treatises, but much of what we know of his philosophy comes in the form of letters. I’ve joked that he invented the calculus on the back of a cocktail napkin in the corporate lounge while his flight from Paris to Hanover was delayed, and that of course was an exaggeration for comic effect.

It wasn’t the calculus, but a dialogue on theology, and it was on a yacht from London to Rotterdam that was held fast in port by headwinds.

Leibniz by profession was a diplomat, and had been recalled from cosmopolitan Paris to dull Hanover several times (generally ignoring the orders to return while searching for academic employment), but on October 4, 1676, he left Paris, not for Hanover, but for London, where he called on various scholars and was entrusted with a letter to Spinoza for personal delivery. A month later, he hitched a ride on the yacht of Prince Ruprecht von der Pfalz, bound for Rotterdam.

From Rotterdam we know that Leibniz traveled to Amsterdam, where he met with many Spinozists, perhaps securing letters of introduction that would facilitate his meeting with Spinoza himself. And sometime around November 18, 1676, Leibniz arrived at Spinoza’s residence in The Hague.

We’ve all played the dinner party game. What famous person/three famous people/learned sages would you like to share a meal with/have a beer with/ask but one question? And here, we have that. The young diplomat and the somewhat older heretic, whom Leibniz described as:

The famous Jew Spinoza had an olive complexion and something Spanish in his face; for he was also from that country. He was a philosopher by profession and led a private and tranquil life, passing his time polishing glass in order to make lenses for magnifying glasses and microscopes.

There are other partnerships and chance meetings in the history of philosophy, but there isn’t a meeting quite this bizarre. It was risky for Leibniz to be associated with Spinoza. There’s not an easy contemporary parallel, but something like a young Republican staffer dining at a known Communist sympathizer’s house during the height of McCarthyism comes close.

So what did they talk about? We think Leibniz stayed with Spinoza from three days to ten. Fourteen years later, Leibniz published a single page, called “That a Most Perfect Being Exists.” In a footnote, Leibniz wrote:

I presented this argument to M. Spinosa when I was at The Hague, who thought it to be sound. Since at first he contradicted it, I wrote it down and read this paper to him.

Spinoza never mentioned the meeting, at least not in anything of his that survived. He died perhaps three months later, of a lung disease that was in all likelihood exacerbated by the fine ground glass that floated in the air as he shaped his lenses.

The resulting influence on Leibniz’s philosophy of Spinoza, and perhaps of this meeting, is at once obvious and hard to trace. Leibniz in some ways defined himself in contrast to Spinoza, and one of the results of trying to avoid Spinozism is that Leibniz backs off of his commitment to the PSR, and thus from rationalism. He ends up with a second principle, the Principle of Contradiction, which is also an independent fundamental principle. It states (in the Monadology):

… in virtue of which we judge that which involves a contradiction to be false, and that which is opposed or contradictory to the false to be true.

The PSR is separate from this. And this means, of course, that the PSR is not something which it would be contradictory to deny. The PSR isn’t a conceptual truth, in other words. But then what grounds it? It can’t be grounded by itself. It can’t be brute…. can it?

Thus, avoiding the consequences of Spinozism comes at a considerable cost; Leibniz must give up full-blown rationalism.

But what of the man to whose philosophy Leibniz defined himself in opposition? While he had harsh and fiery words to say about Spinoza’s philosophy, for the man, he wrote, thirty years after their clandestine meeting:

I know that there are people of an excellent nature who would never be led by doctrines to do anything unworthy of themselves. It can be acknowleged that Epicurus and Spinoza, for example, led entirely exemplary lives.

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26 comments

Henry David Thoreau also made his living grinding something very fine (graphite) and also died of lung disease. He made important contributions to pencil technology. In 1853 the Thoreaus shifted from pencil production to the sale of bulk graphite.

Kafka also died of lung disease (TB), which, although it is not caused by inhalation of anything (well, except TB bacilli) may well have been made worse by his working in his brother’s asbestos factory, and also made an important contribution to industry – he invented the workman’s hard hat.

Sure. The principles are meant to be distinct, which means that one can’t be explained by the other; otherwise, we’d just have one ultimate principle, with the second principle being something that was easily derived from the first.

So if the PSR were something that were contradictory to deny (a basic truth of logic), then it would reduce to being just a special case of the PC. (“The PSR is true just because its contradiction is false, and this follows from the PC, as do many other truths of logic.”) And Leibniz wants to rule that out. The problem is, that this means the PSR can’t be a conceptual truth, and it really looks like the sort of thing that should be a conceptual truth. (And it can’t be a brute fact, because the PSR says there are no brute facts.)

Ah, they are that way because they were intended that way. My thought was that conceptual truths aren’t sufficiently obvious that the contradictory’s incoherence is readily available. (Or: whether the two principles are distinct or not is hard to know!)

When I took a class in early modern philosophy as an undergrad, Spinoza was on the initial reading list. And then they took him away and I ended up returning that book to the bookstore.* I was disappointed in that, even though I knew nothing of Spinoza, and this series makes me even more so.**

_____

*Or I lost it.

**Also disappointing: the TA made the claim, sort of off-hand it seemed, that Hume was the most important of the philosophers we read that semester. I asked why and he couldn’t explain it.

Bingo. If it’s conceptual, it falls out of the PNC, and thus isn’t independent.

Also disappointing: the TA made the claim, sort of off-hand it seemed, that Hume was the most important of the philosophers we read that semester.
Hume I’ve found is the one who seems prima facie most like the philosophers someone in 2008 could have a beer with. Similar commitments and reasoning principles, etc.

Beer might have played into it, but I think the answer he was sort of leading towards, but never made, would have been something along the lines of “Hume is important for lots of reasons that aren’t part of the material for this course [we ended with Hume, started with Descartes], but if you take more modern and/or topical courses, you’ll start to see.”

if it’s a conceptual truth that all conceptual truths follow from pnc, then “there is a conceptual truth that does not derive from pnc” should be a contradiction.

but, as neddy said above, if that’s incoherent, it’s surely not obviously incoherent. it seems to me that the concept of “conceptual truth” and the concept of “truth derived from pnc” are conceptually quite distnct.

part of what makes this dispute unclear, i suspect, is some slippage between “x is derived solely from y”, “x is derived from y and no other logical principles”, “x is derived from y plus some other stuff, maybe including some logical principles”, and “x is derived from a bunch of stuff, but in a way that does not violate principle y”.

i mean, is every theorem that you deduce using modus tollens therefore “derived from modus tollens”? a “special case of modus tollens”? those both seem false to me.

ditto for pnc; i’d imagine there are conceptual truths in which it plays far weaker roles; e.g. ct1 is derived from a bunch of other stuff and uses pnc merely in one step of the derivation; ct2’s derivation never invokes pnc at all, though it also does not violate pnc (though neither does it affirm the consequent or commit a quaternio terminorum).

so i don’t feel like the notions of “x derived from y” and “x distinct from y” are at all clear to me here.

My Modern class started with Bacon and ended with Kant. Seemed like we were both sacrificing depth for breadth and maybe over-reaching the boundaries of the category (moreso with Bacon than with Kant).

i mean, is every theorem that you deduce using modus tollens therefore “derived from modus tollens”? a “special case of modus tollens”? those both seem false to me.

No, but the parallel question here would be whether you’d be able to say that modus tollens isn’t reducible to “negation” and “and”, or was some independent logical principle. If you were to insist that modus tollens an independent principle, you’d be wrong, and we’d show that by showing how it reduced to other logical operators. You’d be right that modus tollens is a great tool, and that we learn how it has its own rules, but if we asked whether it were a fundamental principle, we’d have to say, no, because it’s explainable in terms of something else.

That’s really all that’s going on here. Leibniz can’t escape it by saying ‘well, we only use the PC a little bit” any more than you can say “… but it’s only a little negation.”

The PC just says a) contradictions are always false b) things which are contradictory to false things are always true. It’s the latter part where conceptual truth sneaks in (being the things which are contradictory to false things). And so if I say “why is the PSR true?”, and you say “it’s a conceptual truth”, then what ultimately makes the PSR true is the PC. So then when you say “what’s the fundamental principle?” I say “we have one, the PC.” But Leibniz wants the PSR and the PC both to be fundamental principles.

oh for christ’s sake. i meant ‘modus ponens’ all through those last coupla comments, where i was saying “modus tollens”.

look, as embarrassing as that is, i don’t think it affects my worries, other than showing me up for the amateur i am.

i still think:
a) there are other principles than pnc; and
b) not every thing that is the result of a proof which employs principle y should be said to be “derived from” principle y, much less a “case of” principle y; and
c) even when something can be cast as a “case of” principle y, there are quite different amounts and kinds of other stuff that will need to be added in in order to get from principle y to your conclusion, and the differences matter.

“and we’d show that by showing how it reduced to other logical operators.”

This is an easy Google.

Leibniz would agree that there are other principles besides PNC. And b) and c) aren’t what I’ve been arguing at all, in that we’re not talking about the relationships between proofs that employ principles and their premises, but about relationships between principles.

I can do the reduction to negation and and here (‘v’ stands for ‘or’, ‘->’ is ‘if-then’, ‘~’ is negation):

A v B = ~(~A & ~B)
A -> B = ~A v B (this is how we roll with material implication, if you don’t like this definition I can prattle on for a while about alternatives)

That’s the simple part.

Then, I guess, you have the principles governing &, which are pretty obvious, and reductio ad absurdum, which is that if you assume p and can derive a contradiction q & ~q from it, then ~p holds. We’ll also need that ~~p entails p, which can be seen as another version of the principle of non-contradiction (it’s possible but clunkier to add another version of reductio to obtain the same power).

…so that’s how modus ponens can be seen to be derived from the principle of non-contradiction and maybe principles of conjunction. I think. I’m not sure how this relates to Leibniz, and & can be reduced to ~ and -> in a similar way, so I personally wouldn’t necessarily use this to argue for logical priority.

Right, the analogy only goes so far. But if we were to say we need conjunction, negation, and material implication as the foundation for all of classical logic, we could surely point out that we really only need negation + one of them.

It’s similar to what’s going on with the PSR and the PC. Leibniz wants to say that both are independently required by his system, but it looks his choice are either a) have the PSR reducible to the PC (in which case it’s not independent) or b) have a brute PSR (in which case he has a brute fact.)

When I was in grad school I was surrounded by people who would sneer “Oh, but that proof is in classical logic.” Oh, good times, to wonder if one’s derivation would be acceptable to the intuitionists. -(–p->p)!